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Many perceptual grouping algorithms depend on parameters one way or another. It is always difficult to set these parameters appropriately for a wide range of input images, and parameters tend to be tuned to a small set of test cases. Especially certain thresholds often seem unavoidable to limit search spaces in order to obtain reasonable runtime complexity. Furthermore early pruning of less salient hypotheses is often necessary to avoid exponential growth of the number of hypotheses. In the presented work we show how the adoption of a simple anytime algorithm, i. e. an algorithm which returns the best answer possible when interrupted and may improve on the answer if allowed to run longer, for finding closed convex polygons eliminates the need for parameter tuning. Furthermore it quite naturally allows the incorporation of attentional mechanisms into the grouping process.